Acoustic resonators can be used to implement signal processing functions in various electronic applications. For example, some cellular phones and other communication devices use acoustic resonators to implement frequency filters for transmitted and/or received signals. Several different types of acoustic resonators can be used according to different applications, with examples including bulk acoustic wave (BAW) resonators, such as thin film bulk acoustic resonators (FBARs), solidly mounted resonators (SMRs), stacked bulk acoustic resonators (SBARs), double bulk acoustic resonators (DBARs), and coupled resonator filters (CRFs).
A typical acoustic resonator comprises a layer of piezoelectric material sandwiched between two plate electrodes in a structure referred to as an acoustic stack. Where an input electrical signal is applied between the electrodes, reciprocal or inverse piezoelectric effect causes the acoustic stack to mechanically expand or contract depending on the polarization of the piezoelectric material. As the input electrical signal varies over time, expansion and contraction of the acoustic stack produces acoustic waves (or modes) that propagate through the acoustic resonator in various directions and are converted into an output electrical signal by the piezoelectric effect. Some of the acoustic waves achieve resonance across the acoustic stack, with the resonant frequency being determined by factors such as the materials, dimensions, and operating conditions of the acoustic stack. These and other mechanical characteristics of the acoustic resonator determine its frequency response.
In general, the performance of an acoustic resonator can be evaluated by the values of its parallel resistance Rp, series resistance Rs, quality (Q) factor, and its electromechanical coupling coefficient kt2. The series resistance Rs is the smallest value of magnitude of input impedance of the acoustic resonator, and series resonance frequency Fs is a frequency at which that minimum occurs. The parallel resistance Rp is the largest value of magnitude of input impedance of the acoustic resonator, and parallel resonance frequency Fp is a frequency at which that maximum occurs. The Q-factor is a parameter that quantifies the amount of energy lost in one cycle of oscillations and is defined as a fraction of energy lost to total energy stored in the resonator in one cycle of oscillations. The electromechanical coupling coefficient kt2 is a normalized difference between parallel and series resonance frequencies Fp and Fs and is typically expressed in percent values (%).
Devices with higher Rp, higher Q-factor and lower Rs are considered to have superior performance compared to devices with lower Rp, lower Q-factor and higher Rs. Thus, other things being equal, it is desirable to provide a filter with an acoustic resonator having a higher Rp, higher Q-factor, and lower Rs. Nevertheless, these performance parameters are typically in a tradeoff relationship with other design factors, such as the cost and size of an acoustic resonator. For instance, in some designs, reducing the size of an acoustic resonator to achieve reduced cost may degrade one or more of the performance parameters. Accordingly, there is a general need for improved resonator designs that achieve improvements such as cost and size scaling without unduly compromising performance.